Lagrangian Duality
See also: Dual problemThe Lagrangian dual of a QP is also a QP. To see that let us focus on the case where and Q is positive definite. We write the Lagrangian function as
Defining the (Lagrangian) dual function, defined as, we find an infimum of, using
hence the dual function is
hence the Lagrangian dual of the QP is
maximize:
subject to: .
Besides the Lagrangian duality theory, there are other duality pairings (e.g. Wolfe, etc.).
Read more about this topic: Quadratic Programming
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